Unbias estimators and MSE

timer Asked: Nov 7th, 2014

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Question 4

Let x₁, x₂, …xₓ be a random sample of n i.i.d. observations following the Poisson distribution with parameter (mean) ϴ such that E(Xₐ) = ϴ.  Consider three estimators of ϴ given as:

ϴ₁ = X,     ϴ₂ = X₁,   ϴ₃ = (x₁ + 2x₂)/3

i.)  Show that all the three estimators are unbiased

ii.)  Calculate which of three has the least Variance

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